CAREER CHOICE AND THE RISK PREMIUM IN THE LABOR MARKET

Transcription

1 CAREER CHOICE AND THE RISK PREMIUM IN THE LABOR MARKET German Cubas and Pedro Silos September, 2014 Abstract Is risk priced in the labor market? We document a strong, robust, and positive correlation between average earnings and the variance of both temporary and permanent idiosyncratic shocks to earnings across 21 US industries. However, since workers are heterogeneous in their abilities, the correlation may be entirely driven by selection. What portion of the correlation is compensation for risk and what portion is compensation for unobserved abilities? We construct an equilibrium model with imperfect insurance of labor earnings shocks. The variance of shocks varies across industries. An industry-specific ability drives a worker s comparative advantage, which interacts with her risk aversion to determine an optimal career choice. We find that permanent shocks are highly priced, whereas temporary shocks are not. Two additional results arise. First, workers accumulate different levels of wealth depending on the employment industry. Second, compensation for risk explains a sizable fraction of observed cross-industry differences in labor earnings. Key words: Risk Premium, Labor Markets, Roy Model, Incomplete Markets JEL Classifications: E21 D91 J31. Affiliation: University of Houston, Federal Reserve Bank of Atlanta, respectively. Corresponding author: German Cubas, University of Houston, 204 McElhinney Hall, Houston, TX 77584, USA, gcubasnorando@uh.edu, (Phone), (Fax). We thank G. Canavire for his excellent research assistance and D. Amengual, Y. Chang, M. Bils, F. Borraz, Center for Economic and Policy Research, C. Carroll, M. Deveraux, J. Dubra, J. Hatchondo, G. Kambourov, D. Lagakos, M. Lopez- Daneri, J. Ponce, B. Ravikumar, V. Ríos-Rull, C. Robotti, R. Rogerson, Y. Shin, G. Ventura, and R. Warren for their comments and suggestions. We also thanks the seminar participants at decon FCE-UDELAR, Central Bank of Uruguay, Federal Reserve Bank of Atlanta, Federal Reserve Bank of St. Louis, Federal Reserve Banks of Dallas, University of Iowa, Universidad de Los Andes, Instituto Tecnológico Autónomo de México, National Bureau of Economic Research Summer Institute, University of Georgia, University of Houston, Society for Economic Dynamics Meeting in Seoul, Tsinghua Workshop in Macroeconomics and Quantitative Society for Pensions and Saving workshop at Utah State University. German Cubas thanks the Fondo Clemente Estable of ANII (projct FCE ) for financial support. The views expressed here are those of the authors and do not necessarily reflect those of the Federal Reserve Bank of Atlanta, the Board of Governors or the Federal Reserve System. 1

2 1 Introduction The risk-return trade-off in financial assets has been extensively studied in financial economics and macroeconomics. Much work has been devoted to constructing economic environments whose quantitative predictions match the data. Although the findings of a large empirical literature suggest the labor market is a major source of risk for most workers, to date, a quantitative analysis of the risk-return trade-off in the labor market has not been attempted. As a first attempt, this paper poses and answers the following questions: Are labor earnings positively correlated with their volatility? If so, what does the standard framework for studying imperfect risk-sharing imply for the risk-return trade-off workers face in the labor market? What additional ingredients does the standard framework need in order to match and understand the facts on labor earnings and their volatility? Surprisingly, these questions have never been answered. Answers to those questions would improve our understanding of central topics in labor economics and macroeconomics, ranging from the measurement of risk in the labor market to policy related issues such as redistribution and insurance policies and optimal taxation. We begin by documenting two facts using the Survey of Income and Program Participation (SIPP). The first finding is a large dispersion in the variance (both transitory and permanent) of shocks to labor earnings across 21 US industries: Workers in the construction or durable goods industries experience large permanent shocks to earnings, while those working in social services are insulated from earnings variability. Working for the government entails relatively low permanent risk but high transitory risk. Our second and new finding is a strong, positive, and robust correlation between mean earnings and earnings risk across industries. This correlation is obtained once we control for other industry characteristics that affect the average level of earnings. Perhaps surprisingly, this relationship appears to be about the same regardless of whether the focus is on temporary or permanent risk. The estimated coefficients 2

3 imply a difference in average earnings, solely related to risk, between the riskiest and safest industries of around 5%. When considering transitory shocks, the increase due to risk between earnings of workers in the safest and the riskiest industries is 4%. These correlations must be approached with caution. The study of the risk-return trade-off in labor markets is more complex than in financial markets, and as a result that positive correlation cannot immediately be associated with the existence of a risk premium in labor markets. Since workers are heterogeneous in their abilities and industries value some abilities more than others, the estimated correlation may be driven entirely by selection. In other words, high average earnings in risky industries may reflect the relative scarcity of particular abilities. Workers lacking such abilities would be unable to command high earnings even if they were willing to expose themselves to risk. 1 To quantitatively evaluate the risk-return trade-off in labor markets, our starting point is the workhorse framework used to study risk-sharing in macroeconomics: an equilibrium consumption-savings model in which workers experience shocks (permanent and transitory) to their labor earnings. We introduce a career choice in which different careers represent industries. choose an industry in which to supply labor services. In our environment, risk-averse individuals Some industries are riskier than others and, everything else equal, they are less attractive. These industries are less attractive because shocks to labor earnings are not perfectly insurable. Since this environment says nothing about selection, it attributes any correlation between risk and the average level of earnings to compensation for risk. To account for selection, we assume that workers are ex ante heterogeneous: Each is endowed with an industryspecific ability, which drives a worker s comparative advantage, interacting with her risk aversion to determine an optimal career choice. To summarize, the model over- 1 Selection driven by comparative advantage is only one of the difficulties on which this paper focuses. Among other difficulties may be that workers have different degrees of risk aversion or that high-risk industries are more attractive because of the option value of eventually switching to a low-risk industry (see Neumuller (2014), on this last point). 3

4 laps an Aiyagari (1994) economy, where markets are incomplete, with a Roy (1951) model, where workers self-select into different careers based on their comparative advantage. We confront our model with US data from several sources. Earnings in the model are subject to permanent and transitory shocks. The stochastic processes driving these shocks are the same as those estimated using the SIPP. The parameters driving the industry-specific production functions are from National Income Accounts data. In our benchmark case, we set the risk-aversion parameter to 3 and parameterize the distributions of abilities so that in equilibrium the model delivers the mean and standard deviations of the cross-sectional distributions of earnings observed in the data for each of the industries in the economy. Therefore, by construction, we replicate the documented positive correlation between mean earnings and their volatility. Two important model predictions that are not matched in the calibration process arise and are noteworthy. First, the model predicts a distribution of workers into industries closely resembling the distribution observed in US data. Second, the wealth-to-income ratios predicted by the model for each of the industries are positively correlated with their variance of the permanent shock. This result confirms the findings of Carroll and Samwick (1997): Individuals who work in risky industries save more wealth than those working in safer industries. Viewed through the lens of the model, the positive relationship between the variance of both the permanent and transitory shocks to earnings and the average level of earnings is a convolution of two forces: the compensation for risk and the compensation for industry-specific skills. Therefore, in order to separate the effect of these two forces into the observed differences in mean earnings, we proceed by performing a counterfactual exercise in which we eliminate individual differences in ability or comparative advantage. In other words, we consider individuals as ex ante homogeneous. In this counterfactual world, only the differences in the volatility of earnings across industries shape an individual industry choice. This experiment yields two 4

5 results. First, with the same value for the risk-aversion parameter, the model over predicts the positive correlation between mean earnings and permanent risk (i.e. a risk premium that is higher than in the data). According to this result, the permanent shock to earnings is more important than is deduced from the results of our reducedform empirical relationship. In addition, our model requires the mean ability level of individuals after they are sorted into industries to be negatively correlated with permanent risk. Second, in this counterfactual exercise, the model predicts a temporary risk premium that is much smaller than in the benchmark case. Thus, according to this result, the strong association between the variance of transitory shocks and mean earnings observed in the data (which, in light of the reduced-form model, can be interpreted as a pure risk premium) arises entirely from selection. A large fraction of individuals possess the skills that increase productivity in industries with relatively large transitory shocks. Hence, despite individuals risk aversion, their comparative advantage leads them to work in high (temporary) risk industries. Finally, the model has implications for labor earnings inequality. Overall, inequality is driven almost entirely by shocks, with little effect caused by initial earnings differences implied by workers comparative advantage. Regarding inter industry earnings inequality, about a quarter (26%) is due to cross-industry differences in risk and the remainder is due to differences in abilities. An omission from our model is the possibility that workers switch industries in response to adverse shocks. As an implicit insurance mechanism, allowing for industry switching may have quantitative implications for the degree of compensation for risk. Moreover, the option to switch increases the appeal of starting a career in a risky industry. Partly in response to this omission Neumuller (2014) emphasizes the switching option as a way to obtain a negative relationship between earnings risk and mean earnings. Neumuller (2014) finds a negative relationship using biennial earnings data from the Panel Study of Income Dynamics (PSID). His empirical result contrasts with 5

6 that reported by Dillon (2012), who uses the same data. We revisit this topic in the appendix and show there is no evidence in the SIPP that transitions from risky to safe industries among the young are larger than those from safe to risky industries. Related Literature To our knowledge, the first attempt to empirically analyze the link between the variability of income and mean earnings was the seminal work of Kuznets and Friedman (1954) in their classic study of income of professionals. In the early 1980s, Abowd and Ashenfelter (1981), Feinberg (1981), and Leigh (1983) continued this work. This earlier literature focused on the cross-sectional dispersion of earnings, rather than the variation of earnings over time, and did account for earnings risk due to changes in employment status. Feinberg (1981) considers variation of income over time but uses a very small subset of the PSID to estimate the relationship between risk and earnings. 2 Moreover, all these authors interpret their empirical results as proof (or lack thereof) of the existence of a risk premium or compensating differential, with no mention of the possibility of selection influencing the empirical findings. Finally, they do not distinguish between transitory and permanent shocks to earnings. Carroll and Samwick (1997) test the hypothesis that households whose members are employed in high-risk industries accumulate more precautionary wealth; our results confirm this finding. One important contribution of our paper is that we measure idiosyncratic labor market risk by industry and its macroeconomic implications in a general equilibrium framework. On the measurement side, we build on papers such as those by Storesletten, Telmer, and Yaron (2004b), Guvenen (2009); and Low, Meghir, and Pistaferri (2010); but we extend this literature by explicitly considering different industries. On the modeling side, our work belongs to the extensive quantitative macroeconomics literature with heterogeneous agents and incomplete markets initiated by Bewley (1977), Huggett (1993), and Aiyagari (1994). More recent contributions 2 He has annual earnings data for only 326 individuals whom he follows for 6 years. 6

7 include those by Storesletten, Telmer, and Yaron (2004a) and Heathcote, Storesletten, and Violante (2008, 2009). The analysis of heterogeneity in the ability levels of individuals or comparative advantage and its effect on career choice goes back to Roy s seminal work in 1951 (Roy (1951)). In this vein, our work contributes to a growing literature that develops quantitative models of occupational choice and income dynamics. One important related paper is by Kambourov and Manovskii (2009), who study the interplay between occupational mobility and wage inequality. Even though we focus on industries instead of occupations and we abstract from mobility, our work can be considered as complementary to theirs. 3 We highlight a source of wage inequality that is still intimately related to individuals choice of occupational/industry. More recently, in a work contemporaneous to ours, Dillon (2012) finds a positive relationship between the expected value and variance of lifetime earnings. Aside from the different methodology and dataset used by Dillon, our framework, (i) incorporates the industry choice of workers in a general equilibrium model and (ii) explicitly models the interplay between unobserved abilities and aversion to risk, which are absent in Dillon s work. Nevertheless, she uses a richer econometric model and, more importantly, her results complement and confirm our main empirical finding. Finally, as mentioned, our framework incorporates workers comparative advantage and its effect on occupational choice, thus it is closely related to Roy s (1951) work. The empirical content of the original Roy model is studied in Heckman and Honore (1990) and Buera (2006). Roy s ideas are also adapted in modern dynamic discrete choice models to analyze the sources of income inequality first, in an important paper, Keane and Wolpin (1997) and more recently in Hoffmann (2010). However, we consider our work as the first that integrates Roy s ideas into the analysis of career choice under uninsurable idiosyncratic labor earnings risk in a general equilibrium model. Along these lines we see our framework as a useful tool to be applied in fu- 3 In the appendix, we discuss the relationship between industry and occupations in our data set. 7

8 ture work incorporating workers comparative advantage into the analysis of earnings dynamics and wage inequality. 2 The Story in a Simple Static Model This section illustrates the main forces at work by using a simplified version of the full quantitative model presented in Section 4. Our economy is populated by a mass of risk-averse individuals of unit measure. Individuals live for only one period, each period has one unit of time to be supplied inelastically in a competitive labor market. There is a representative firm that produces a consumption good according to the following constant returns to scale technology: Y = (L 1 ) φ (L 2 ) 1 φ. (1) where Y denotes output, L 1 and L 2 represent two types of labor inputs required to produce output, and φ is the share of type-1 labor. Individuals may supply only one type of labor. If a worker chooses to supply type-1 labor, she earns the wage rate for that type, w 1. Alternatively, supplying type-2 labor brings w 2 zγ in earnings. w 2 is the wage rate for type-2 labor and z > 0 indicates a type-2 labor-specific skill or ability, distributed as G(z, θ). Finally, γ is a shock to labor earnings such that γ = 1 m with probability p and γ = 1+m with probability (1 p) with 0 < m < 1. When choosing the type of labor to supply, workers know their ability but do not know the realization of γ. The level of ability z drives a worker s comparative advantage when supplying type-2 labor. Moreover, workers supplying type-2 labor experience higher variability in earnings than those supplying type-1 labor. Hence, if workers are risk averse, type-2 labor appears less attractive than type-1 labor. The optimal supply of labor maximizes utility. Therefore, 8

9 j = argmax{v 1, V 2 (z)} (2) with j {1, 2}. The two value functions are defined as and ( V 1 = u w 1), (3) [ ] [ ] V 2 (z) = p u(w 2 z(1 m)) +(1 p) u(w 2 z(1+m)), (4) where u the utility function with u c > 0 and u cc < 0. The aggregate level of each type of labor results from individuals choices: L 1 = G(z, θ), (5) L 2 = E γ zdg(z, θ), (6) z where z is the level of z such that if z > z, individuals choose type-2 labor and if z z, they choose type-1 labor. As a result, the average level of earnings for type-1 labor is and that of type-2 labor is e 1 = w 1, (7) e 2 = w2 z zdg(z, θ) 1 G(z, (8), θ) where w 1 and w 2 are the marginal products of the two types of labor, which in a competitive labor market are equal to the wages for each type of labor. 9

10 Figures 1 through 6 summarize the analysis in this section. The figures depict a simple numerical example illustrating the mechanisms at work in the model. 4 Individuals values of supplying type-1 and type-2 labor as a function of z are represented by the curves V 1 and V 2 in Figure 1. V 1 is independent of z and thus is a constant. By contrast, V 2 is strictly increasing in z; the crossing point of the two determines z. Individuals whose ability levels are below z choose to supply type- 1 labor and those with ability levels above the threshold supply type-2 labor. This ability threshold determines the mass of both types of individuals and, hence, the aggregate levels of L 1 and L 2. In the model, mean earnings and uncertainty in earnings are positively correlated. Figure 2 shows the mean earnings of type-2 relative to mean earnings of type-1 labor as a function of uncertainty: Higher levels of uncertainty (x-axis) imply higher average earnings. In other words, the market compensates risk-averse individuals for bearing risk. What is the underlying mechanism that generates this feature in the model? Figure 3 shows the changes in the equilibrium value of z for different values of the variance of the shock to labor earnings. Higher uncertainty increases the ability level of the marginal worker (z ), decreasing the mass of workers who supply type-2 labor. Both a higher z and a lower supply of workers increase average earnings (because of decreasing returns to scale in production). 5 Figure 4 illustrates the effect of changing the distribution of abilities on the relationship between uncertainty and mean earnings. The figure shows mean earnings for type-2 labor as a function of uncertainty (as in Figure 2), but for different values of the mean of ability, E(z). In particular, we assume E 1 (z) < E 2 (z) <... < E 5 (z). 6 4 It is assumed that the utility function is of the logarithmic type, G(z, θ) is the cumulative distribution function of a gamma random variable Γ(κ, θ) (where θ = (κ, θ)) with κ = 20 and θ = 4, φ = 0.5, and p = Here, the magnitude of the changes in the equilibrium value of z depend on the value of φ. 6 The variance of ability is kept fixed throughout. This is achieved by changing the parameters of the gamma distribution. 10

11 Different values of E(z) yield different curves summarizing the relationship between the earnings and the level of risk. As the expectation increases, those curves shift up. Suppose that each distribution of abilities represents an industry (or an occupation). Moreover, suppose that the level of uncertainty in earnings varies across industries. Our simple model shows that it is the interaction between the distribution of abilities (or changes in the distribution of comparative advantage) and the uncertainty in earnings that determines the sorting of workers into different industries. This sorting, in turn, determines the relationship between average earnings and earnings uncertainty. As an example, assume that mean ability levels are positively correlated with the variance of the shock to labor earnings (i.e., the higher the E(z) for an industry, the higher is σγ). 2 The observed combinations of uncertainty and mean earnings are represented by the red line in Figure 5. As a result, a positive correlation between the mean and the volatility of earnings arises. However, suppose that in contrast, mean ability levels are negatively correlated with the variance of the shock to labor earnings. The red line in Figure 6 shows the correlation between mean earnings and earnings volatility is now negative. Notice that the level of compensation for risk remains the same (as summarized by the increasing relationship between earnings and uncertainty in any given industry). In other words, even if the data show a negative correlation between mean earnings and uncertainty, that correlation says little about the pricing of risk in the labor market. What appears to be ex ante a counterintuitive relationship between mean earnings and earnings volatility can be explained by the interaction of the risk compensation (risk premium) and the distribution of abilities (comparative advantage). The goal of this paper is to estimate such a relationship (see Section 3) and decompose it into a comparative advantage component and a risk premium component using a structural model (see Section 4). 11

12 3 Labor Market Risk and Mean Earnings In this section, we briefly describe our dataset. Then we document that risk and return in earnings are positively correlated across industries. We do this in two steps. First, we estimate the labor earnings processes and the properties of the shocks faced by workers in different industries. Second, we characterize and estimate the empirical relation between mean earnings and the degree of uncertainty in earnings across industries. Our definition of labor earnings is rather broad (but consistent with previous studies). In addition to the obvious variability in wage rates, we also consider changes in earnings due to changes in the number of hours worked or changes in employment status. 7 We focus on individuals who never change industries as this is most consistent with the quantitative framework we use. 3.1 The SIPP To explore the relationship between the level of average earnings and the degree of unforeseen variability in those earnings, we turn to the data. Ideally, to obtain an accurate answer, researchers would hope for an extended high-frequency, large panel of individual labor earnings with characteristics describing both the employee and the employer. The richer that dataset, the easier it would be to separate risk from other features that could affect average earnings. For the United States, the SIPP is the best approximation of that ideal dataset. The SIPP is constructed by the U.S. Census Bureau and takes the form a series of continuous panels that follow a national sample of households. The first panel began in 1983 but the earlier panels had a short duration. In 1996 the Census Bureau began constructing longer panels with a larger number of households (more than 30,000, although the actual size varies); and these panels are the ones on which we focus. More specifically, we use the 1996, 2001, and 7 We do not consider individuals who move in and out of the labor force, but we do consider employment to unemployment transitions and vice versa. 12

13 2004 panels obtained from the Center for Economic and Policy Research, CEPR (2014). The SIPP conducts interviews every four months, eliciting information at monthly frequency on variables such as labor earnings, demographic characteristics, occupation, and so on. It follows individuals for 16 quarters; this short duration prevents us from having entire life-cycle profiles of earnings. 8 SIPP variables are collected for at most two jobs, but the survey also asks which is the primary job for the individual. The appendix provides a step-by-step description of our choice of the sample of individuals on which we perform the analysis described in this section. In brief, we (i) focus on the reported primary jobs of married individuals between 22 and 66 years of age (ii) eliminate those who are self-employed, (iii) simultaneously report missing earnings but positive hours worked, (iv) those out of the labor force, and (v) do not report complete samples. In addition, we define earnings to include unemployment insurance if an individual reports zero hours worked and is unemployed. There are two main advantages to using SIPP data. 9 number of respondents. The first advantage is the The SIPP dataset is considerably larger than that of the PSID, which surveys about 10,000 households, or the NLSYs, which interview between 9,000 and 13,000 individuals. The second advantage is the interview frequency. The SIPP provides a wealth of information at a monthly frequency; the PSID interviews annually (biennially since 1997) and the NLSY97 has also been biennial since Fortunately, for many individuals in the United States unemployment or declines in income are short-lived experiences (usually weeks or few months). But given these are the risks on which this study focuses, that fact underscores the importance of the availability of information at higher frequencies. 8 The short panel duration is still long enough to accurately estimate the variance of permanent shocks to earnings. The appendix provides a Monte Carlo analysis showing that the variance can still be estimated accurately provided the cross section is large. Moreover, the SIPP data were also used by Low, Meghir, and Pistaferri (2010) to estimate the variance of permanent shocks using a specification almost identical to ours. 9 See Abowd and Stinson (2011) validation studies comparing SIPP s good-quality earnings data compared with administrative data. In addition, Gottschalk and Huynh (2006) studied the SIPP relative to other longitudinal panels such as the Panel Study of Income Dynamics (PSID) and the National Longitudinal Survey of Youth (NLSY97 and NLSY79). 13

14 3.2 Labor Income Shocks The first step in our analysis computes earnings variability at the individual level with a regression approach used extensively in the literature, see for example, Carroll and Samwick (1997). We proceed by estimating a fixed effects model for each industry j in our sample. Given a panel of N individuals for whom we measure earnings (and other variables) over a period of time T, we assume that (log) earnings for individual i in industry j at time t, y ijt can be modeled as y ijt = α ij + β j X ijt + u ijt (9) The vector X includes several variables that help predict changes in the level of log earnings. Specifically, we include age, sex, ethnicity, years of schooling, an occupational dummy, and time dummies. We assume that the error term, u ijt, is distributed i.i.d. N(0, σ 2 j,u ).10 We estimate equation (9) for all individuals in a given industry. Repeating this procedure for all industries yields estimates {ˆα ij, ˆβ j } 21 j=1 and σ j,u 2. We present the estimates of the variances of the innovations for each industry in Table 1 and Figure 7. The median of the estimated variances is 0.026, which corresponds to volatility in the personal services industry. The workers who face the least amount of uncertainty are those in the armed forces, social services, agriculture and forestry, business services, and education. 11 Workers in mining, hospitals, durable goods manufacturing, medical services, and other services face the highest levels of income uncertainty. 12 According to this notion of risk, the riskiest industry is almost 50% riskier than the safest one. Finally, we test the hypothesis that all the estimated variances are equal 10 Below we add persistence to the error term process. 11 The armed forces may be considered risky using alternative metrics (e.g., injuries and death while in service). 12 Income is top-coded in SIPP; this feature of the data probably leads us to underestimate the risk of industries such as Finance. 14

15 and reject it with a high degree of certainty. 13 Although the differences in variances across industries do not appear large in magnitude, depending on the persistence of the shocks and workers risk aversion, they may imply large differences in welfare. To account for this difference in the nature of risk, we enrich our empirical analysis by allowing the error term to be decomposed into a permanent component and a transitory component. Transitory shocks (e.g., the loss of an important customer for a consultant) are seldom a cause for concern; small levels of savings are usually enough for workers to weather such shocks successfully. Permanent shocks last longer and can be associated with, for instance, depreciation of job-specific human capital or permanent changes in how industry operates. Smoothing out the latter type of shock through a buffer stock of savings is more difficult and permanent changes in consumption are often required. We follow Carroll and Samwick (1997) and Low, Meghir, and Pistaferri (2010), among others, by assuming that u ijt = η ijt + ω ijt, (10) where η ijt, the transitory component, is distributed i.i.d. N(0, σ 2 j,η ), and ω ijt, the permanent component, is a random walk, that is, ω ijt = ω ij,t 1 + ǫ ijt (11) with i.i.d. innovations ǫ ijt that are distributed N(0, σj,ǫ 2 ). By estimating equation (9), we obtain {{û ijt } N j i=1 }T t=1. We estimate the variances of the permanent and transitory components by following the identification procedure proposed by Low, Meghir, and Pistaferri (2010). Specifically, taking first differences in equation (9) and given the process specified in (10), we have 13 We use the Welch ANOVA test to test this hypothesis. 15

16 y ijt = β j X ijt + η ijt + ǫ ijt. (12) Now define g ijt = (y ijt β j X ijt ) = η ijt + ǫ ijt. (13) To identify the parameters of interest, we compute and E(g 2 ijt ) = σ2 ǫ ij + 2σ 2 η ij (14) E(g ijt g ijt 1 ) = σ 2 η ij. (15) To estimate the variances of the two innovations, we proceed as follows. For an individual i in a given industry j, we estimate Ê(g2 ijt ) and E(gijt g ijt 1 ) by taking the sample moments. By solving the system, we obtain σ 2 ǫ j and σ 2 η j by taking averages across individuals of the estimated variances obtained for each individual. 14 Table 2 and Figures 8 and 9 show the estimated variances for each industry. The median of the estimated variances across industries is for the permanent shock (column 2, corresponding to Utilities) and for the transitory shock (column 4, corresponding to Communication) This decomposition uncovers large differences across industries in the degree of permanent and transitory income volatility. Interestingly, the variance of the permanent component across all industries is higher than that of the transitory component 14 The short time dimension of the SIPP does not prevent us to obtain good estimates of the variance of the shocks since it contains a large sample of individuals. This is discussed in the appendix in which we show the results of a Monte Carlo experiment using our estimators. 15 The Welch ANOVA test leads us to reject the hypothesis of equal variances for both type of shocks. 16 Our estimates are in the upper bound of the range of values presented in the literature (see Dillon (2012), Low, Meghir, and Pistaferri (2010) and Carroll and Samwick (1997)). However, the comparison is complicated by the fact that we use total earnings instead of earnings per hour and our data are at quarterly frequency instead of annual. 16

17 by a factor of 2.5. As described in Table 3, in some industries both permanent and transitory uncertainties are large (above median), which is the case for mining, utilities, wholesale trade, and other services. There are also relatively safe industries, (i.e., the variance of both the permanent and transitory shocks is below the median); these are agriculture and forestry, non-durable goods manufacturing, and the armed forces. For the remaining industries, workers in construction, communication, business services, personal services, recreation and entertainment, and education face high permanent but low transitory risk. Finally, workers in transportation, retail trade, finance, hospitals, medical services, social services, and government face high transitory but low permanent risk. 3.3 Correlation Between Earnings and Risk Having estimated measures of risk for our group of industries, we are now ready to test the hypothesis that the level of risk and the average level of earnings across industries are positively correlated. Our claim, however, should be understood as a ceteris paribus claim. That is, everything else constant, a higher level of risk should be associated with a higher level of earnings. Of course, not everything else is constant across industries. Industries differ along many dimensions that may affect average earnings independently of their level of risk. This should raise suspicion that either the mix of workers or firms in a given industry is an important determinant of the industryât s average level of earnings. Therefore, we estimate the relationship between earnings and earnings risk in two different ways to account for this industry heterogeneity. The first approach involves computing industry averages (that is, averages across individuals who work in a given industry) of variables we deem relevant in determining average earnings. To estimate the relationship between average earnings and industry risk, we estimate the following regression equation: y = γ+θz+ ν, (16) 17

18 where y is a vector whose jth element is the average (log) earnings for individuals in industry j, and Z is a matrix of regressors. The jth row of Z has seven elements: average age, average age squared, the average level of education of all individuals working in industry j, the fraction of females in industry j, two dummies that represent two of the three panels of the SIPP used in the estimation, and the industry j variance of income shocks estimated above (see Table 1). Since the number of industries in each of the panels of our sample is 21, y is a column vector of dimension 63 and Z is of dimension Finally, γ is a vector of intercepts and ν is a vector of residuals. We assume that the error term, ν j, is distributed i.i.d. N(0, σ 2 ν). Column 2 of Table 4 shows the results of estimating equation (16). It presents the estimated values for the coefficients and their probabilities of being less than zero computed by bootstrapping. All coefficients are significant and have the expected signs. Workers age and education levels are positively related to mean earnings and females labor earnings are on average lower than those of males. It is worth noting that the dummies representing the different SIPP panels are also significant showing the effect of the different years in the mean earnings as well as differences in the structure of the data panels in for instance, the number of households covered. Our focus is on the sign and magnitude of the coefficient associated with risk, σ 2. The table shows that this coefficient points to a strong and positive association between uncertainty and earnings. More importantly, the probability that this coefficient is less than zero is around 10%. Note that the value of the coefficient associated with uncertainty implies that the increase in the mean level of earnings associated with the change in the variance from the safest industry to the riskiest (armed forces to mining) is around 5%. According to this econometric model, this result would be consistent with the existence of a risk premium in the labor market We also estimate equation (16) when the matrix Z includes the variances of the temporary and permanent components of income shocks. In that case, the matrix Z has 9 columns because we do not include the vector of overall variances. 18 We also estimate equation (16) by defining earnings in per hour terms; our results are robust to this specification. See the appendix for details. 18

19 The second approach to estimating the relationship between industry risk and mean earnings involves estimating earnings net of an individual s main observed characteristics: age, age squared, level of education, and gender. following pooled regression, We estimate the y ijt = γ 0 + γx ijt + λ ijt. (17) The vector of coefficients γ represent the effect of the observed characteristics (age, age squared, level of education, and gender) on earnings. These coefficients are common across individuals and across time. We use these estimates to compute net earnings at the individual level: ỹ ijt = y ijt ˆγX ijt. Averaging across time and across individuals in each industry gives the mean of net earnings by industry. Formally, for a given industry j, we compute where ỹ j = 1 N j N j ỹ ij, (18) i=1 ỹ ij = 1 T T ỹ ijt. (19) t=1 We regress average net earnings by industry on volatility of earnings to estimate the relationship between earnings and volatility: ỹ j = α 0 + α 1 σj 2 + α 2 I α 3 I νỹ,j. (20) The number of left-hand-side observations is 63 (21 for each of the three panels). α 0 is an intercept, α 1 is the coefficient that relates risk to (net) earnings, α 2 and α 3 are the coefficients that represent the dummies for the 1996 and 2001 SIPP panels, respectively, and νỹ is the residual, which is assumed to be i.i.d. N(0, σνỹ). 2 Column 3 of Table 4 shows the estimated values for the coefficients and the proba- 19

20 bilities that they are less than zero computed by bootstrapping. Note that, confirming the existence of a risk premium, the coefficient associated with risk, α 1, is also large and positive. According to this approach, the value of the coefficient associated with uncertainty (3.735, see Table 4) implies that moving from the safest industry to the riskiest is associated with a 4% increase in the mean level of earnings net of observables. For the same reasons outlined above, we consider the decomposition of the process into a temporary and a permanent component. We estimate equation (16) using the variances of the two components, permanent and transitory as regressors, instead of just one variance that reflects overall uncertainty. The second column of Table 5 presents the results. All coefficients are significant and have expected signs. With the exception of the coefficients associated with the variances, their magnitudes are close to those found earlier. For the coefficients associated with uncertainty, we first observe that they are strongly positive and have probabilities of being less than zero of 1% and 9% for the permanent and transitory shocks, respectively. The estimated value for coefficients associated with the variance of the permanent shock to earnings is 8.0. Therefore, according to this result, moving from the social service industry (the safest) to construction (the riskiest industry) implies a 6% increase in mean earnings. For the transitory shock, the value estimated for its associated coefficient is 2.5 and so, according to this result, switching from the armed forces (the safest industry) to hospitals (the riskiest industry) implies a 2% increase of in mean earnings. As for the total variance of earnings, we present the results by using our alternative specification to document the relationship between mean earnings and uncertainty (shown in column 3 of Table 5). Again, the estimation results point to a strong and positive relationship between mean earnings and the estimated variances. The values of estimated coefficients for the permanent and transitory shocks to earnings are 7.1 and 7.4, respectively, with very low probabilities of being less than zero: and 0.021, respectively. Accord- 20

21 ing to these results, considering the permanent shock to earnings, moving from social services to construction implies a 5% increase in mean earnings. If we look at the transitory shock to earnings, moving from the armed forces to hospitals implies a 4% compensation in mean earnings. The data and our approach to linking labor earnings and their uncertainty yield estimates that appear consistent with a compensating differential for risk in the labor market. But, as noted in Section 2 caution is necessary. The distribution of average earnings across individuals in an industry is an endogenous outcome resulting from individuals decisions of where to supply their labor services. The level of earnings risk is certainly a factor individuals consider when making that choice. But their comparative advantage, in other words, their relatively higher productivity in a certain industry, which is consequence of a set of individual characteristics, plays a role as well. Some portion of that comparative advantage originates, for instance, from being a female or a college graduate, characteristics that we have accounted for to some degree. Much of the advantage, however, originates from unobserved characteristics, which are obviously difficult to control for. How much of the estimated positive risk-earnings correlation is due to a compensating differential and how much is due to self-selection? In the next section, we use a quantitative framework in which comparative advantage and individuals industry choice are explicitly modeled to determine the answer. 4 The Model Our economy is populated by a mass of risk-averse individuals of total measure equal to 1. Time is discrete and individuals live for S periods, which corresponds to their working lives. In other words, they are born into a labor market and never retire. Each individual is endowed with one unit of time each period that is supplied inelastically in the labor market. When an individual reaches time S+1 and dies, another age 0 21

22 individual replaces her, so the total population is constant. At the beginning of their lifetimes, individuals choose to work in one of J mutually exclusive job opportunities indexed by j, which we interpret as industries. At birth, prior to the industry choice, each individual draws a value for an industry-specific skill or ability from a given distribution specified below. These skills directly affect the productivity and, hence, earnings of an individual, thereby determining an individual s comparative advantage for, say, working in finance and not in agriculture. Since these skills are random draws, we are silent about their origin but they could loosely be interpreted as innate abilities or human capital acquired before entering the labor market. Finally, the values for the industry-specific skills neither grow nor decrease over an individual s lifetime. Once individuals are working within a particular industry (from which they cannot move), they are subject to idiosyncratic shocks to their labor income. The process driving these shocks differs from industry to industry, and workers in some industries experience a higher variability in earnings than workers in other industries. If workers are risk averse, riskier industries look less attractive. When an individual is born in period 0 (i.e., when she enters the labor market), her problem is to choose one of the J mutually exclusive career alternatives to maximize the expected discounted value of her lifetime utility: {[ S } E 0 β s 1 1 j u(c s,j ),] Ω i,0, s=1 j where 1 j is an indicator function with value 1 j = 1 if the individual chooses to work in industry j and 0 otherwise. The function u(c s,j ) denotes the individual s per-period utility derived from choosing j J and consuming c s,j ; we assume u c > 0 and u cc < 0. The only source of uncertainty are shocks to labor earnings as described in detail below. For now it suffices that expectations in equation (1) are taken with respect to the distribution of such shocks. The vector Ω i,0 represents the information set of an 22

23 individual i at time 0; formally, it is the vector Ω i,0 = { } θ i,1,..., θ i,j, where the logarithm of each value θ i,j is drawn from an industry-specific distribution N(µ θj, σθ 2 j ). Each period, by inelastically supplying one unit of time to industry j, each individual receives labor earnings, w j θ i,j e ν i,j, composed of an industry-specific competitive wage rate (w j ), individual-specific industry pre-labor-market skills (θ i,j ), and an individual-specific but time-varying labor productivity shock (ν i,j ). Once the individual makes her industry choice, only the θ corresponding to the chosen industry affects her lifetime labor earnings. For an individual of age s, the time-varying component of earnings is the addition of two orthogonal stochastic components: ν s,j = η s,j + ω s,j, (21) where η j is an i.i.d. transitory shock to log earnings distributed as N( 2 1 1, σ 2 σj,η 2 j,η ) and ω s+1,j is the permanent component that follows a random walk: ω s+1,j = ω s,j + ǫ s,j where ǫ j is N( 1 2 1, σ 2 σj,ǫ 2 j,ǫ ) i.i.d innovations. By subscripting the variance by j, we clarify that the nature of the shock process is industry specific.) Despite the inability of consumers to change industry in midlife, we allow them to partially insure against labor income shocks by saving in a one-period risk-free non contingent bond with an exogenous interest rate equal to r. Individual s Decision Problem Suppose an individual has chosen an industry in which to supply labor and has begun her working life. Every period, optimization for this individual entails choosing how much to consume and the amount of savings or quantity of one-period bonds to purchase. 19 The variables relevant to these 19 Our model differs from others in the literature in the optimal choice of an industry and its general equilibrium implications. Once the individual has chosen an industry, the optimization problem of 23

24 decisions are the level of wealth (b), the age of the individual (s), and the following components of income: the time-varying component (ω and η) and the ability level for the chosen industry (θ j ). Thus, the vector of individual state variables can be denoted as x = (b, ω, η, s, θ j ), where j is the chosen industry. Denote by Ψ j (x) the distribution of industry j workers across assets, age, income, and abilities. 20 It is an aggregate state variable since it determines the wage rate in industry j. Only the marginal distribution of age is identical across all industries. For convenience, let S = S B S Eη S Eω S θ {1,..., S} denote the state space of the vector of state variables x. 21 It is convenient to write the problem recursively, and we denote the remaining lifetime utility for an age- s individual working in industry j by V j (x s = s). It is defined by { } V j (x s = s, Ψ j ) = max u(c)+βev j (x s = s+1, Ψ c,b j ) if 1 s S and 0 o/w, subject to c+b = w j (Ψ j )θ j e η e ω + b(1+r) (22) and ahead. b b, b 0 = 0, b S+1 0. (23) We follow relatively standard notation when x denotes the values of x one period Equation (22) is a standard flow budget constraint that equates consumption plus savings to total earnings from capital holdings, b(1 + r), and earnings from the consumer is essentially identical to many examples in the literature analyzing heterogeneousagent economies. The only departure is that we allow two different shocks with different statistical properties. This departure allows us to analyze the impact of transitory and permanent risk on industry choice. 20 The distribution is subscripted by j because workers, facing different income shocks and selfselecting into industries based on different ability levels, will choose different levels of assets. 21 In general, the joint state space should have a subscript j. In our model, the borrowing constraint and longevity are identical across industries. Income innovations and abilities are all real numbers; hence, we can omit the subscript j. 24

25 supplied labor, w j (Ψ j )θ j e ν. In addition to this budget constraint, individuals face a borrowing constraint that restricts the lower bound on asset holdings. Also, individuals are born with zero wealth (b 0 = 0) and face a non negativity constraint in their savings at the time of death (b S+1 0). At birth, the individual chooses from a set of J industries the one that yields the highest utility. where W j for an individual i is defined as j = argmax { W 1,..., W J }, (24) { } W j = E 0 Vj (x s = 1) Ω i,0. (25) When choosing an industry, Ω i,0 (the vector of abilities drawn at birth) is in an individual s information set, thus appearing to the right of the conditioning sign. The individual also knows the statistical properties of shocks experienced by workers in each industry. As a result, although not explicitly written, it should be understood that the expectation is taken with respect to a different distribution if the worker computes W j for j = j. The choice in equation (24) induces an endogenous distribution of workers across industries. Let µ j denote the mass of workers in industry j with J j=1 µ j = 1. Firms Our model economy can be pictured as a small, open economy consisting of a set of islands in which each island represents an industry. Each industry produces a consumption good according to the following industry-level technology: Y j = N α j j, (26) where Y j is the output of industry j, N j represents the labor input of that industry 25